Density functional theory's utility in studying phase behavior of adsorbed species is well established, and when coupled with atomistic thermodynamics it can provide reasonable estimates for adsorption behavior at finite temperatures and pressures. Unfortunately DFT suffers from two serious limitations: the first is that the calculations are expensive to perform, and the second is that there is an inherent uncertainty in their results. The computational expense of DFT calculations limits how many configurations can be directly studied using DFT, and with no way to predict lowest-energy structures without means of a direct calculation, it is never possible to be certain that the most stable structures have been identified using DFT. The uncertainty in the results means that even if one structure is deemed more stable than another due to having a lower calculated DFT energy, if the predicted energy difference is within the statistically uncertainty of the DFT calculations, their real ordering cannot be determined. Because of the effect these limitations have upon phase diagrams predicted through DFT calculations, we have explored means to deal with them by using our DFT results to parameterize a cluster expansion. The ease and speed with which cluster expansions can be performed on a virtually unlimited variety of adsorbate configurations allows for a much more broad spectrum of configurations to be considered, reducing the probability that a stable structure has been missed, while statistical analysis can be used to predict the magnitude of errors in the predicted energies.

Using DFT have we studied adsorption of oxygen on gold and platinum FCC (111) surfaces, with coverages of up to a full monolayer. We found strong coverage dependence in the adsorption energies on these surfaces, which can be attributed to modification of the d-band caused by the presence of the adsorbate atoms. These effects, while differing between the platinum and gold surfaces, were both found to be linear, which in turn resulted in a linear relationship between the adsorption energies of a single configuration on both surfaces. Direct enumeration of our cluster expansion for all configurations of up to 15 FCC hollow sites confirmed this linear trend, and also resulted in many configurations that were close in energy to the predicted ground states. From our error calculations these configurations were shown to be statistically indistinguishable from the stable structures. Based on our statistical analysis we cannot identify, with certainty, which configuration is the true ground state structure. We will discuss some strategies we are developing to examine how these statistically degenerate structures are related to one another.